Topological Effect on the Anderson Transition in Chiral Symmetry Classes

In this Letter, we propose a mechanism of an emergent quasilocalized phase in chiral symmetry classes, where the wave function along a spatial direction with weak topology is delocalized but exponentially localized along the other directions. The Anderson transition in two-dimensional chiral symmetry classes is induced by the proliferation of vortex-antivortex pairs of a U(1) phase degree of freedom, while the weak topology endows the pair with a Berry phase. We argue that the Berry phase induces spatial polarizations of the pairs along the topological direction through the quantum interference effect, and the proliferation of the polarized vortex pairs results in the quasilocalized phase.